It may be that all the key people are sitting around the negotiating table. This would be most unusual.
The union secretary has to report back to his committee and ultimately the union members. An executive might have to report back to the chief executive or the board.

An outcome that might seem satisfactory to those in the room might look very different to others who were not involved in the give and take of the negotiation but only see the final result.

Very often a leader wants to look good to his or her followers. People do not like to be seen to have backed down. Saving face might be important. All these things need to be considered and designed into the outcome.

Not all people are reasonable. Some people are show-offs. It is not a matter of wishing that people were perfect but of dealing with known imperfections.